Displace does not work on images as planes
You are using a different version of Blender than what is used in the tutorial. I believe in older versions of Blender the default displacement texture that gets added when you press 'New' on the modifier is a 'Clouds' texture, which causes the displacement. In newer versions of Blender it seems that the default texture that is added is an 'Image' texture, but until you actually load an image in the texture panel, nothing will happen, hence no immediate displacement.

You should be able to just continue with the tutorial as normal. In the next step he actually explains how to change the texture type from 'Clouds' to 'Image' anyway. When he explains how to do this you can just change it to 'Clouds' for a second to see that you are in fact getting the same results.